Problem: Multiply the following complex numbers: $({2+2i}) \cdot ({-2})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2+2i}) \cdot ({-2}) = $ $ ({2} \cdot {-2}) + ({2} \cdot {0}i) + ({2}i \cdot {-2}) + ({2}i \cdot {0}i) $ Then simplify the terms: $ (-4) + (0i) + (-4i) + (0 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -4 + (0 - 4)i + 0i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -4 + (0 - 4)i - 0 $ The result is simplified: $ (-4 - 0) + (-4i) = -4-4i $